On Synchronization Control Of Multi-layer Complex Network With Uncertain Coupling

Complex network is a complex aggregate of some interlinked and interactive units with some characteristics and functions.Recently,complex network has become highly active,with many new systems being studied in.application areas such as math,biology and computer science.Synchronization problem is one of the most demonstrating topics in complex networks.Multi-layer network phenomenon exists a lot in the world,Therefore it is significant to study synchronization control problem for multi-layer networks.In this thesis,by using the nonlinear system theory,classical control theory and matrix analysis,based on the multi-layer network,three types of synchronization problems i.e.uncertain coupling,nonlinear coupling,node and coupling time-varying delay and cluster synchronization are investigated.The main work can be summarized as follows:Firstly,for a class of Multi-layer network with uncertain coupling,considering the situation about nonlinear coupling,a feedback controller is designed.Based on Lyapunov stability theory,a sufficient stability condition is given.In the case of two and three layers about the multi-layer complex network,Numerical simulation results show that the proposed controller can achieve complete synchronization for the complex network in a very short period of time with many Lorenz chaotic systems as its nodes.Secondly,in view of complex networks with node time-varying delay and each layer coupling time-varying delay,a feedback controller is designed.Based on Lyapunov stability theory,a sufficient stability condition is given.In the case of two and three layers about the multi-layer complex network,Numerical simulation results show that the proposed controller can achieve complete synchronization for the complex network in a very short period of time with many Chen chaotic systems as its nodes.Thirdly,for a class of Multi-layer network with cluster,considering the situation about uncertain coupling,nonlinear coupling,node and coupling time-varying delay,an adaptive feedback controller is designed.Based on Lyapunov stability theory,a sufficient stability condition is given.Numerical simulation results show that the proposed controller can achieve complete synchronization for the complex network in a very short period of time with many Lorenz chaotic systems and Rossler chaotic systems as its nodes.Finally,the main work of this thesis is summarized and some future research directions are put forward.